The present invention relates to television special effects devices, and more particularly to special effects using polar image coordinates to produce a new class of television special effects.
Images are manipulated in digital picture manipulator (DPM) systems by mapping pixels from their original positions in a raster to other positions in a new raster. Usually this is accomplished by applying a mathematical function to the address (defined by a pair of coordinates) of each pixel. The function returns a new coordinate pair for the pixel. The two pairs of coordinates form a map relating the original position to the new position. Two general map types exist: a forward map and a reverse map. The forward map uses the original pixel coordinates as arguments to the mapping function. The function returns the address to which the pixel is to be moved. A forward mapping function answers the question--for each pixel in the image where does it go in the new output image? A reverse map is the opposite case. Coordinates from the output image are used as arguments to the mapping function. The mapping function returns coordinates in the input image from which the pixel comes. A reverse mapping function answers the question--for each pixel in the output image where do I go in the input picture to get the pixel? The reverse mapping system is the dominant implementation used in current DPM systems.
In video applications pixels normally are transferred in an ordered fashion known as scan line order. Pixels transfer from upper left to lower right of the image. The pixel addresses with respect to the screen can then be generated with simple counters that are incremented and reset by the normal video blanking signals. This X-Y addressing method is inherently a rectangular coordinate system. The mapping functions operate on these counter generated X and Y coordinates to produce the new mapped coordinates. The mapping function determines what the image will look like after the transformation. Implementation of a mathematical operation on these addresses is performed by dedicated hardware. The more complex the function, the more complex the hardware. Certain mathematical operations are fairly simple to implement, such as algebraic addition and multiplication, while others are more difficult, such as division, trigonometric and logarithmic functions and the like. Usually linear operations are implemented directly with adders and perhaps multipliers. Non-linear operations are usually implemented with lookup tables based in a memory device, either ROM or RAM. Hitherto, the polar to rectangular, and back, transformation set required non-linear operations of square roots and trigonometric and inverse trigonometric functions to be performed with an accuracy well beyond the practical application of lookup table techniques, and so were never really considered as possibilities to be used in mapping functions.
Thus what is desired are special effects using polar coordinates that are practical and can be used in either forward or reverse mapping functions.